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13th World Conference on Earthquake EngineeringVancouver, B.C., Canada

August 1-6, 2004Paper No. 497

PERFORMANCE-BASED SEISMIC DESIGN AND BEHAVIOR OF A

COMPOSITE BUCKLING RESTRAINED BRACED FRAME

Prabuddha DASGUPTA1, Subhash C. GOEL

2, Gustavo PARRA-MONTESINOS

3, and K. C. TSAI

4

SUMMARY

The concept of Buckling Restrained Braced Frames is relatively new and recently their use has increased

in the U.S., Japan and Taiwan. However, detailed design provisions for common practice are currently

under development. Since the summer of 2002, researchers at the University of Michigan (UM) have

been working cooperatively in a joint study with research team at the National Center for Research onEarthquake Engineering (NCREE), Taiwan, involving design, analysis and full scale testing of such a

frame by pseudo-dynamic method.

The selected structure is a three story, three bay frame consisting of concrete-filled-tube (CFT) columns,

steel beams, and composite buckling restrained braces. The frame was designed using an Energy-Based

Plastic Design procedure recently developed by co-author Goel at UM. The method utilized selected

target drifts (2.0% for 10% in 50 year and 2.5% for 2% in 50 year design spectra for this frame) and

global yield mechanism. Because of the need for more precise control of design clearances between theend connections and steel casing of the braces, buckling restrained braced frames are excellent candidates

for application of this newly developed design methodology.

The paper briefly presents the energy-based approach developed at UM as well as a modal displacement-

based design procedure adopted by the research team at NCREE for calculation of design base shear for

the frame. Results from inelastic response analyses of frames deigned by the two methods for a Taiwan

earthquake are compared. The same frame was also designed for a U.S. location and analyzed underground motions scaled for U.S. standards. The frames designed by the UM approach exhibited

satisfactory dynamic responses for both Taiwan and U.S. ground motions.

INTRODUCTION

Excellent seismic behavior of buckling restrained braces (BRBs) (Tsai [1]) encouraged an experimental

program at the National Center for Research on Earthquake Engineering (NCREE), Taiwan, in

conjunction with analysis and design studies by researchers in the U.S. at the University of Michigan. In

1Ph.D. Candidate, University of Michigan, Ann Arbor, MI

2Professor, University of Michigan, Ann Arbor, MI

3Assistant Professor, University of Michigan, Ann Arbor, MI

4Professor, National Taiwan University, Taiwan

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this program, the BRBs provide the primary seismic resistance mechanism to a 3-story 3-bay frame,

tested under pseudo-dynamic loading at NCREE in October 2003. General layout of the prototype

building is shown in Figure 1a, while a view of the test frame is shown in Figure 1b. For design purpose,

two of such frames were assumed to resist the total seismic force for a 3-story prototype building. The

seismic frames are indicated by thick lines in Figure 1a.

DESCRIPTION OF TEST FRAME

The frame was designed to resist the seismic loading through two separate mechanisms. The primary

resistance is provided by buckling restrained braces in the central bay of the frame (Figure 1b). This bay

is designed to act as a purely braced frame with all beam-to-column and brace-to-column connections

made as simple (pinned) connections. The braces are designed to resist 80% of the total seismic force for

each seismic frame, while 20% of the load is resisted by the two external bays, designed as moment

frames with moment connections at the joints of exterior beams and columns. All columns are made of

concrete filled tubes. Different sections are chosen for interior and exterior columns, while keeping thesame size along the building height. Wide flange sections are used for beams. Different beam sizes are

used at different floors, while keeping the same size in all the bays at each floor.

4@23ft

6@23 ft

4@23ft

6@23 ft

3@23 ft3@23 ft

(a) (b)

Figure 1: (a) Layout of the prototype building, (b) View of the test frame

BUCKLING RESTRAINED BRACE PROPERTIES

Buckling restrained braces are typically made by encasing a steel core member in a concrete filled steel

tube (Figure 2a). The steel core is kept separated from the concrete filled tube by a layer of unbonding

material applied on the surface of the steel core. The role of concrete encasing and steel tube is to prevent

buckling of the steel core, so that a well formed load-displacement response of the brace is achieved

under large displacement reversals. The unbonding material ensures that the force coming into the BRB is

carried by the core only, without engaging the encasing material. Different configurations of BRBs were

tested at NCREE under large reversed cyclic axial loading and an optimum configuration was selected foruse in the test frame (Tsai [1]) (Figure 2a). A typical load-displacement response obtained from the

selected BRB configuration is shown in Figure 2b. As can be seen, full hysteretic loops and excellent

energy dissipation were achieved. However, it is to be noted that the yield load reached in compression

was about 10% higher than that reached in tension. This needs to be accounted for while designing the

frame.

Seismic frame

3@13ft

BRBs

4@23ft

6@23 ft 3@23 ft

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(a) (b)

Figure 2: (a) Configuration of the BRB adopted, and (b) Typical load-displacement behavior of a BRB

(From Tsai [1])

DESIGN CONSIDERATIONS

A comparative study is presented on the behavior of three prototype frames designed to meet common

performance criteria through different design procedures. The first frame was designed by the research

team at NCREE. For this frame, calculation of base shear was done following a multi-modal

displacement-based seismic design (DSD) procedure and the guidelines stipulated in the 2002 Draft

Taiwan Seismic Design Code. Design of that frame was done by elastic method. The second frame wasdesigned by the team at University of Michigan. In this case, same base shear as calculated by the

NCREE team was assumed. However, a plastic design procedure, recently developed by Goel, wasadopted to design the frame (UM Frame 1). The third frame (UM Frame 2) was designed for a base shear

calculated by following a simple energy-based procedure developed at UM (Leelataviwat [2], Lee [3]).

Frame design was done by the plastic design method as used for UM Frame 1.

The basic design parameters were selected by the research team at NCREE following the 2002 Draft

Taiwan Seismic Design code. Total seismic weight of each floor was divided equally between the two

seismic frames. The seismic weights applied on each frame were as follows,

1st

and 2nd

Floor: 714 kips, and 3rd

Floor: 564 kips

In order to calculate the design base shear for the prototype building, two performance criteria were

considered and the one that resulted in higher design base shear was chosen for the design of the test

frame. In the first performance criterion (Life Safety), maximum roof drift was set at 0.02 radian when thebuilding is subjected to an earthquake that has a 10% probability of exceedance in 50 years (10/50). In the

second performance criterion (Collapse Prevention), maximum roof drift was set at 0.025 radian for a

2/50 seismic event. A real ground motion time history was scaled by appropriate factors to represent the10/50 and 2/50 events. Scaling was done by considering the 5% damped Pseudo Spectral Acceleration

(PSA) of a SDOF system with period T=1 sec. The scaling factors were determined by equating this

spectral acceleration to the corresponding values prescribed in the draft Taiwan seismic code for 10/50

and 2/50 events at a hard rock site. The two resulting time histories have PGA values of 0.461g and

0.622g, respectively.

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For the purpose of frame design and for performing the push-over analysis, the total base shear needs to

be distributed over the three floor levels. The force at i-th floor was calculated by using the following

equation:

dN

i

ii

iii V

m

mF

=

=

1

, (1)

where iim and are the mass and target displacement, respectively, of the i-th floor, and dV is the total

design base shear. The relative floor forces obtained are as follows:

1st Floor: 0.11, 2nd Floor: 0.365, and 3rd Floor: 0.525

DESIGN BASE SHEAR

Taiwan DesignA brief description of the NCREE procedure to arrive at the design base shear is presented in this section.

A detailed description of this procedure can be found elsewhere (Tsai [1]).

In the first step, the frame was idealized as a MDOF system with three degrees of freedom. ModalContribution Factors (MCF) for the three modes, as well as their modal masses and modal story drifts,

were then computed. Since, for this particular frame, the contributions from the 2nd

and 3rd

modes (MCF =

0.008 and 0.002, respectively) were insignificant compared to the contribution from the 1st

mode (MCF =

0.99) (Tsai [1]), only the 1st

mode was considered for design purposes. Thus, the three floor

displacements of the 1st

mode were used to obtain an effective system displacement eff associated with

the modal target roof drift.

In the next step, the ductility demand for the 1st

mode of the frame was computed. Because 80% of the

seismic force was to be carried by the braced frame, yield drift of the effective system was computed

based on the drift at the point of brace yielding and increased by 25% to account for the contribution from

the moment frame. From the target maximum story drifts, ductility demand for each story was calculated

and a simple average was taken as the effective ductility demand for the system. Using this ductilitydemand, and from the effective target displacement

eff , the effective time period of the system was

obtained from the inelastic displacement spectrum of the ground motion considered. Corresponding

effective stiffness effK value of the system was computed from this time period.

Finally, the base shear required at the point of target drift was computed by simply multiplying effK

by eff . This ultimate base shear was reduced to the yield base shear by assuming a bi-linear load-

displacement curve with a strain hardening of 5% and the ductility demand as computed earlier. This

yield base shear served as the design base shear (Vd) of the frame. Of the two performance criteria, the

base shear computed from the second criterion governed and was equal to 415 kips.

UM DesignThe base shear was re-calculated by using a procedure developed at UM (Leelataviwat [2], Lee [3]),

where a fraction of the peak elastic input energy of an earthquake to a structure is equated to the energyneeded by the structure in getting pushed up to the maximum target displacement. The procedure is

briefly described below.

In the first step, the base shear-roof displacement profile of the frame was modeled by an idealized tri-

linear curve, as shown in Figure 3. This tri-linear curve was obtained by considering the base shear-roof

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displacement profiles of the braced frame and the moment frame separately. Both of these profiles were

idealized by elastic-perfectly plastic responses. Roof drift of the braced frame at yield point can be easily

calculated from the geometry of the frame. As mentioned earlier, the base shear carried by the braced

frame at this point was assumed as 80% of the total design base shear Vd, which is an unknown at this

stage. Based on past analysis results, roof drift of the moment frame at yield was assumed as 2%, carrying

the remaining 20% of the total base shear. These two bi-linear curves were superimposed to obtain the tri-

linear load-displacement curve of the whole frame (Figure 3). This tri-linear curve was further simplifiedto a bi-linear curve (Figure 3) by equating the areas under the two curves. The design ductility

demand for the frame was calculated from this curve.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3

Roof Drift (%)

BaseShear/Vd

Figure 3: Idealized frame responsesfor Collapse Prevention criterion

In the next step, the peak input energy was calculated by considering an elastic SDOF system and by

using the equation given by Housner [4], as shown below,

2

2

1vMSE= , (2)

where vSM and are the total mass and the pseudo spectral velocity of the system, respectively. However,

for an inelastic system, this equation needs to be modified (Figure 4a). Thus, a modification factor was

applied to Eqn. (2) to estimate the energy needed to push the idealized elastic-perfectly plastic system to

the selected target displacement, as shown in Figure 4a. Applying this modification factor and converting

vS to spectral acceleration gCe , the modified required energy, mE , can be re-written as,

2

22

1

= em C

TWgE

, (3)

where Wand T are the total weight and the fundamental period of the system, respectively. eC is the

maximum base shear coefficient. Following the seismic provisions of IBC 2000 [5], the value ofTfor the

3-story frame was estimated as 0.37 sec. Using this period, eC was obtained from the design responsespectra given in the Draft Taiwan Seismic Code (2002) for the two considered hazard levels. The value of

was obtained from the T relationship (Figure 4b) proposed by Leelataviwat [2].

The modified input energy, mE is then equated to the total work done by the seismic forces applied to the

frame as it is pushed to the target drift as shown in Figure 4a. For this purpose, a bi-linear load-

displacement behavior (Figure 4a) and a linear distribution of the floor displacements along the height of

the frame were assumed. A distribution of floor forces, as mentioned earlier, was also assumed. From this

Idealized tri-linear curve

Simplified bi-linear curve

Brace yielding

Moment frame yielding

BaseShear/Vd

% Roof Drift

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0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3

Period (sec)

s=2

s=6

s=5

s=4

s=3

energy balance equation, design base shear dV was obtained. As with the Taiwan method, the base shear

computed from the second criterion (2.5% drift for 2/50 earthquake) governed and was equal to 340 kips,

which is significantly smaller than that obtained from the Taiwan method.

(a) (b)

Figure 4: (a) Energy input in elastic and inelastic systems, (b) Energy modification factorsagainst period

UM PLASTIC DESIGN METHODOLOGY

The research team at the University of Michigan adopted a simple plastic design procedure to design the

test frame. Designs of the bracing part and the moment frame were done independently from each otherwith an 80-20% sharing of total base shear between the two components.

Material PropertiesMaterial properties used for the design and analysis of the frame were kept the same as those used in the

Taiwan design. All steel sections: core member of the braces, wide flange beams and steel tubes of the

CFT columns, had nominal yield strength of 50 ksi with bi-linear stress-strain curves. Strain hardening

ratios of 4% for beams and columns, and 2% for the brace members were considered. Additionally, a 10%overstrength was considered for the expected yield strength of steel for the beams and columns. However,

no overstrength was considered for the brace members, because the material for the braces was to be

tested before their fabrication in order to get an accurate measure of its strength, and its effect was to be

incorporated by adjusting the cross-sectional areas of the braces. The concrete used for the CFT columns

was assumed to have a strength of 5000 psi.

Design of Moment FrameThe moment frame was designed for 20% of the total base shear, to be carried by the exterior columns

and the exterior beams. The design of the frame was done following the guidelines provided in a relatedresearch by Leelataviwat [2] and Lee [3], and using the proposed plastic design methodology. Designs of

the columns and beams were done simultaneously to balance the member capacities, so that a desired

yield mechanism is achieved. The design steps are described below.

As a first step, a desired failure mechanism was selected. The assumed failure mechanism consisted of

beam-column junctions developing plastic hinges only in the beams at all three floors, and a plastic hinge

at the base of each column (Figure 5a). Thus, strong column-weak beam philosophy was followed. It

should be mentioned that the design strength of the columns was calculated only from the steel tube

section, neglecting the contribution from the concrete core.

y eu ma

Base Shear

21 ME=

Drift

CyW

CeW

E EE +

Period (sec)

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An initial required strength of the column section was estimated from the consideration of avoiding the

possibility of a story mechanism in the first story. This was done by considering the base shear to be

resisted by a story mechanism in the first story, i.e., the columns in the first story forming plastic hinges at

both ends (Figure 5b). Minimum required flexural capacity of the columns was obtained by equating the

overturning moment due to the shear carried by the columns to the combined design capacity of the

plastic hinges at the ends of the columns. A 10% margin of safety was also considered. A square tubular

section with strength greater than the required strength was then assigned to the columns. Since the samecolumn section was continued along the full height, story mechanisms in the upper stories were

automatically avoided.

Required flexural strengths for the beams were calculated in the next step. Beam strengths were

determined by assuming a scenario where the moment frame is acted upon by its full share of base shear,distributed at the three floors as described earlier, and having developed plastic hinges in all three beams

and at the base of the columns (Figure 5c). Thus, the total resisting moment provided by the capacity ofthe plastic hinges in the beams and column bases was equated to the total overturning moment of the

applied floor forces. This, however, produced only one equation, whereas three beam strengths needed to

be determined. This was dealt with by assuming the flexural capacities of the beams at the three floors to

be proportional to the applied story shears (Figure 5c). The required flexural strengths of the beams were

then calculated and available wide flange sections with strengths closest to the required strengths wereselected.

(a) (b)

(c)

Figure 5: (a) Moment frame yield mechanism, (b) Minimum column strength from story mechanism, and(c) Moment demands on beams

As a last step, the expected beam strengths with strain hardening and the applied floor forces were used to

calculate the moment demands on the column at the beam-column joints to ensure that no plastic hingeformed in the column at any location.

~

~

~~

~

~

hM

C

MC

MC

MC

0.2 Vd

0.2 Vd

~

~

~~

~

~

hM

C

MC

MC

MC

0.2 Vd

0.2 Vd

~

~

~~

~

~

hM

C

MC

MC

MC

0.2 Vd

0.2 Vd

MC

M b

1.7Mb

1.9Mb

hM C

M b

1.7M b

1.9M b9.1 kips

30.3 kips

43.6 kips

MC

M b

1.7Mb

1.9Mb

hM C

M b

1.7M b

1.9M b

hM C

M b

1.7M b

1.9M b9.1 kips

30.3 kips

43.6 kips

0.2Vd

0.525(0.2Vd)

0.365(0.2Vd)

0.110(0.2Vd)

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Design of Braced FrameAs mentioned earlier, the braced bay of the frame was designed to resist 80% of the total lateral forces.

Design of the braced frame involved design of the braces, the interior beams and the interior columns.

Since all connections in the braced frame were assumed pinned, the applied shear force in each story was

resisted by the pair of braces only. Because the bases of the interior columns were assumed to be fixed,

these columns act as cantilevers and carry some amount of shear as the frame undergoes lateral drift.However, for simplicity and to be conservative, this effect was neglected. Thus, cross-section area of the

braces in each story was obtained by simply considering the horizontal component of the design yield

forces of the two braces and equating that to the corresponding story shear, as shown in Figure 6.

The interior beams were assumed as pin connected to the interior columns at both ends, while the bracesconnect at the beam midspan. The beams were designed for a combination of axial force and bending

moment. As the frame drifts, one brace goes into tension and the other into compression. Horizontalcomponents of these forces represent the axial load applied at the midspan of the interior beam. Vertical

components of these forces tend to cancel each other. However, since the yield strength of the

compression brace is assumed to be 10% higher than that of the tension brace, an unbalanced upward

force remains once both braces have yielded, causing bending moment in the beam. Thus, the interior

beams were designed as simply supported beams with an axial load and a transverse load applied at thecenter, as shown in Figure 6. The wide flange sections used in the exterior beams were checked against

this combined loading following the provisions of the AISC steel design manual [6], and were found

adequate for use in the braced frame.

1.1P

1.1PP

P

2.1Pc os

0.1Psin

Psin 1.1Psin

1.1P

1.1PP

P

2.1Pc os

0.1Psin

Psin 1.1Psin

Figure 6: Forces in braced frame after yielding

Design of the interior columns was done primarily from axial load consideration (Figure 6). Columns in

any story carry the vertical components of the brace forces from the stories above. Thus, interior columnsin the 1

ststory were designed for an axial force which is the sum of the vertical components of the brace

forces from the 2nd

and 3rd

stories. Brace forces were calculated at the point when the frame is at its

assumed target drift of 2.5%. Also, the higher yield load of the compression brace compared to that of the

tensile brace, as mentioned earlier, was considered. However, there are some other factors that affect theload on the interior column. These are:

1. Shear force on the exterior beams is transferred through the pinned connection and acts as axial load

on the interior columns. From the deflected shape of the frame, it is seen that this shear force always acts

in the opposite direction to the force coming from the braces, thus reducing the net load on the column.

2. Shear force on the interior beams adds a small tensile load on both interior columns.

0.1Psin2.1Pcos

1.1PP

1.1PP

1.1PsinPsin

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3. Interior columns carry some shear and bending moment by virtue of their bent shape.

For simplicity of design, the above factors were neglected.

COMPARISON OF UM FRAMES WITH TAIWAN FRAME

The cross-section areas of various members obtained from the two UM designs and from the Taiwandesign are shown in Table 1. It can be seen that the UM Frame 1 had almost identical member sizes as

those in the Taiwan frame. Some differences can be seen in the sizes of the beams at all three floors -

those in the UM frame being lighter than those in the Taiwan frame. While the difference is small at the

1st

and 2nd

levels, the beams at the 3rd

(roof) level in the UM frame were significantly lighter than those in

the Taiwan frame. The UM Frame 2, being designed for a significantly smaller base shear, was much

lighter than the other two frames.

Table 1: Membercross-section areas (in2) of frames for Taiwan site

Taiwan Frame UM Frame 1 UM Frame 2

1st

Floor 5.12 5.34 4.60

2nd

Floor 4.50 4.75 4.10

Braces

3rd Floor 2.64 2.80 2.41

1st

Floor 20.0 20.0 20.9

2nd

Floor 20.0 20.0 20.9

Exterior

Columns

3rd

Floor 20.0 20.0 20.9

1st

Floor 18.4 18.4 15.0

2nd

Floor 18.4 18.4 15.0

Interior

Columns

3rd

Floor 18.4 18.4 15.0

1st

Floor 17.1 16.2 13.3

2nd

Floor 14.6 13.5 11.8

Beams

3rd

Floor 12.7 9.13 7.68

FRAME DESIGNED FOR U.S. EARTHQUAKES

To further the study on applicability of the energy-based approach to calculate design base shear, the

same frame was re-designed for a U.S. location (UM-US). Seattle was chosen as the site for the frame.For design purpose, an increased triangular profile of lateral forces, as specified in IBC 2000 [5], was

used. The frame was designed to meet the performance criterion of 2.5% target roof drift in a 2/50 seismic

event. Using a spectral acceleration of 1.98g for a 2/50 event, the design base shear Vd was computed as680 kips. Table 2 shows the member sizes obtained for this frame.

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Table 2: Membercross-section areas (in2) of frame for Seattle site

Braces Exterior Columns Interior Columns Beams

1st

Floor 9.18 30.4 15.0 29.1

2nd

Floor 7.46 30.4 15.0 24.0

3rd

Floor 4.04 30.4 15.0 12.6

PUSH-OVER ANALYSIS

Static push-over analyses were performed on the first three frames as a first step in evaluating and

comparing their behavior. SNAP-2DX program, developed at the University of Michigan for non-linear

static and dynamic analysis of 2D frames (Rai [7]), was used for this purpose. The push-over analysis was

done under displacement-control mode and the frames were pushed to about 3% roof drift with the lateralloads being applied at three floors in the same ratio as the design distribution of the base shear. This ratio

was maintained while the controlling roof displacement applied to the frame was increased. Thedisplacement of the roof was increased in steps of 0.05 inch. Lateral load at any floor was distributed

equally at all five nodes. i.e., four beam-column joints and one brace-beam joint. BRBs were modeled

using a simple truss element with bi-linear load-displacement relationship. The truss element had acompression capacity 10% higher than its tension capacity, and 2% strain hardening. The beams and the

CFT columns were modeled using a beam-column element. Bi-linear moment-rotation curves with 4%

strain hardening were assumed for these members. Appropriate P-M interaction relations for the beam-

column elements were also used. The resulting push-over curves obtained for the three frames were

compared with the load-displacement curves originally assumed in the design stage. Locations and

sequence of yielding were noted and compared for the three frames.

DYNAMIC ANALYSIS

Dynamic analyses were carried out on all the frames by subjecting them to scaled real ground motions

using the SNAP-2DX program. All the ground motions used represented seismic events with 2%

probability of occurrence in 50 year intervals. The ground motion time history used to analyze the framesdesigned for the Taiwan site was obtained by appropriate scaling of a record from the Chi-Chiearthquake. UM-US frame was subjected to three ground motions selected from those recommended by

SAC for a Seattle site. Some characteristics of the selected ground motions are given in Table 3. Framemembers were modeled as in the push-over analysis. A 5% viscous damping ratio was considered. Floor

masses were distributed equally at the five joints at each level.

Table 3: Characteristics of 2/50 ground motions

MagnitudeDistance(miles)

Scale factorDuration

(sec)PGA(g)

SpectralIntensity

(in.)

1999 Chi Chi 7.3 - 2.87 45.0 0.62 1291992 Erzincan 6.7 1.24 1.27 20.78 0.61 130

1949 Olympia 6.5 34.8 4.35 79.98 0.82 115

1985 Valpariso 8 26 2.9 99.98 1.57 179

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DISCUSSION OF RESULTS

Push Over AnalysisFigure 7a shows the base shear vs. roof drift push-over curves for Taiwan Frame and UM Frame 1, which

were designed for the same base shear. Displacements at which yielding occurred at various locations of

the frames are also indicated on the curves. These curves are superimposed on the basic load-

displacement curve constructed from the design base shear (415 kips) and ductility demand (11.4) asmentioned earlier, and by using a 4% strain hardening. As it can be seen from the figure, static load-

displacement behaviors of the two frames are almost identical, with the UM frame carrying slightly

higher force. Also, push-over curves are in excellent agreement with the assumed bi-linear curve, as can

be seen from Figure 7a. Figure 7b shows a similar push-over curve for UM Frame 2, which was designed

for a lower base shear as calculated by the UM method. The pushover curve is superimposed on theidealized tri-linear curve, which was obtained by adjusting the design tri-linear curve (shown in Figure 3)

for overstrength and strain hardening. The two curves are seen to be in good agreement.

The locations and sequence of yielding are seen to be similar in all three frames (Figure 8). Yielding

occurred at the intended locations only. However, at 2.5% roof drift, none of the frames achieved the

complete mechanism. Also, for all three frames, the ratio of base shear carried by the moment frame and

the braced frame were very close to the design ratio of 1:4.

(a) (b)Figure 7: (a) Push-over curves for Taiwan Frame and UM Frame 1, and (b) Push-over curve for UM

Frame 2

(a) (b) (c)Figure 8: Locations and sequence of yielding - (a) Taiwan Frame, (b) UM Frame 1, and (c) UM Frame 2

1

1

1

2

2

2

34 6

8

9 8

10

7

5

1

1

1

2

2

2

34 6

8

9 8

10

7

5

1

1

1

2

2

2

34 6

7

8 8

9 9

7

5

1

1

1

2

2

2

34 6

7

8 8

9 9

7

5

% Roof Drift

BaseShear(kips)

0

100

200

300

400

500

600

700

0 0.5 1 1.5 2 2.5 3 3.5

UM 1

Taiwan

Assumed curveDesign base shear (Vd)

0

100

200

300

400

500

600

700

0 0.5 1 1.5 2 2.5 3 3.5

% Roof Drift

BaseShear(kips)

% Roof Drift

BaseShear(kips)

1

1

1

2

2

2

3 44 5

6 6

7 7

8 9

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Dynamic AnalysisVarious aspects of the dynamic behavior of the three frames for the Taiwan site are shown in Figures 9a

through 9d. Maximum values at three floors, however, did not necessarily occur at the same time instant.

The three frames behaved in a very similar fashion. From the plots of maximum floor displacements

(Figure 9a), it is clear that the lateral displacement profile of all three frames followed a linear pattern.

However, the maximum roof drifts for Taiwan Frame and UM Frame 1 were below the target roof drift of

2.5%, and were about 2.1%. The third frame (UM Frame 2) performed more closely to the intendedperformance level and reached a roof drift of 2.6%. From the plot of maximum story displacements

(Figure 9a) and maximum inter-story drifts (Figure 9b), it is evident that the three floors of all three

frames underwent a fairly synchronized motion, indicating a predominantly first mode of vibration. UM

Frame 2, did show some irregularity as the maximum drift of the second story exceeded the 2.5% limit to

reach to almost 2.8% drift (Figure 9b). However, time history of the floor displacements showed thatthere was only one time instant when this exceedance occurred. At all other time instants, the third frame

also showed uniform story drifts as the first two frames.

0

1

2

3

4

0 2 4 6 8 10 12 14Max. floor displacement (in.)

FloorNo

Taiwan FrameUM Frame 1UM Frame 2

0

1

2

3

4

0 1 2 3Max. interstory drift (%)

Story

No


(a) (b)

0

1

2

3

4

0 100 200 300 400 500Max. floor force (kips)

FloorNo


0

1

2

3

4

0 200 400 600 800Max. story shear (kips)

Story

No


(c) (d)

Figure 9: Dynamic response parameters of three frames for Taiwan site

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0

1

2

3

4

0 2 4 6 8Max. floor displacement (in.)

FloorNo

ErzincanOlympiaValpariso

0

1

2

3

4

0 1 2Max. interstory drift (%)

Story

No


0

1

2

3

4

0 500 1000 1500Max. floor force (kips)

FloorNo


0

1

2

3

4

0 500 1000 1500Max. story shear (kips)

Story

No


From the plot of story shears (Figure 9d), it is seen that the maximum base shear is significantly higher

than that obtained from the push-over analysis for all three frames. This may be attributed to the

significantly different floor force distribution obtained from the dynamic analysis (Figure 9c) compared to

what was assumed for the design of the frames and for the push-over analysis. This was verified by using

the floor force distribution at the time instant when the maximum base shear was reached, and performing

a push-over analysis with that force distribution.

Figures 10a through 10d show selected response parameters from the dynamic behavior of the frame

designed for a Seattle site (UM-US) when subjected to three different ground motions representing 2/50

seismic events. The frame remained well within the target roof drift of 2.5%, reaching 1.56%, 1.48%, and

1.51% (Figure 10a) for the Erzincan, Olympia and Valpariso ground motions records, respectively. As

observed in the previous three frames, this frame also exhibited approximately uniform drift over thethree stories for the three ground motions, as seen from Figures 10a and 10b. Further, a very different

floor force distribution from that assumed for the design of the frame was seen for three three groundmotions (Figure 10c), with lower floors carrying larger forces. Again, this can be the reason for larger

base shears (Figure 10d) than that calculated for design. As can be observed from Figures 10c and 10d,

the more the deviation of the floor force distribution from the design distribution, larger the base shear

carried by the frame.

(a) (b)

(c) (d)Figure 10: Dynamic response parameters of frame UM-US for three Seattle ground motions

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SUMMARY AND CONCLUSION

Results from the seismic analysis of frames with buckling restrained braces are presented in this paper.

Two frames were designed by using a plastic design procedure proposed at the University of Michigan

(UM) by the co-author Goel. The third frame was designed by researchers at NCREE, Taiwan. These

three frames were designed for a site in Taiwan. The first UM frame, as well as the Taiwan frame were

designed for a base shear calculated by using a modal displacement-based procedure, while the secondUM frame was designed for a base shear calculated through an energy-based method developed at UM.

These designs and analyses formed the foundation of the testing program performed at NCREE to

evaluate the seismic performance of buckling restrained braced frames at full scale. A fourth frame was

then designed for a U.S. site to validate the applicability of the energy-based design method for this type

of frames.

The 3-story 3-bay full scale frame was a combination of braced frame and moment frame, where thebraced frame carried most of the lateral force. Two performance criteria were considered for the design of

the frames in the Taiwan site: 2% roof drift for a 10/50 earthquake, and 2.5% roof drift for a 2/50

earthquake. A real ground motion time history, scaled by appropriate factors, was used to represent the

two seismic events. Design base shear was calculated for both performance criteria and the governing

base shear and corresponding performance level were chosen for design. Push-over and dynamic analyseswere carried out on these three frames. The frame at the U.S. site was designed only for the criterion of

2.5% drift in a 2/50 event. Three ground motions representing 2/50 earthquakes were applied to this frame

to study its dynamic response.

The Taiwan Frame and UM Frame 1 had almost identical frame member sizes, and as a result, similar

pushover and dynamic responses were observed. In the dynamic analysis, inter-story drifts in the three

stories were quite uniform. Maximum roof drifts were below the design roof drift of 2.5%. The UM

Frame 2 was significantly lighter, and marginally exceeded the target roof drift. Nearly uniform inter-

story drifts were observed in this frame also, even though a slight non-uniformity was encountered at the

peak roof drift.

The Taiwan Frame and UM Frame 1 were designed for the same seismic force, 80% of which was carriedby the braced part of the frame. Different design approaches followed by the Taiwan team (elastic) and

the UM team (plastic) made little difference in the sizes of the braces. Main difference was in the member

sizes of the moment part of the frame. However, while designed to resist only 20% of the base shear, the

moment frame did not have any significant influence on the overall frame response. As a result, very

similar inelastic response under push-over as well as dynamic analyses was observed.

UM Frame 2 was designed for a significantly smaller base shear, and as a result, was much lighter than

the previous two frames. This frame reached a maximum roof drift of 2.6% in the dynamic analysis, very

closely meeting the target roof drift.

UM-US frame also performed satisfactorily under all three selected ground motions. Roof drift remained

well within the 2.5% limit and the three floors exhibited nearly uniform drifts.

ACKNOWLEDGEMENT

The research work on the U.S. side has been supported by the Earthquake Hazard Mitigation Program of

the National Science Foundation under the direction of Dr. S. C. Liu and more recently Dr. StevenMcCabe (Grant Nos. CMS-9905804 and CMS-0336339). Financial support for the Taiwan side research

program has been primarily provided by the National Science Council (NSC92A06000000-19). The

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opinions expressed in this paper are those of the writers and do not necessarily reflect the views of the

sponsors.

REFERENCES

1. Tsai KC, Weng YT, Lin ML, Chen CH, Lai JW, Hsiao PC. Pseudo Dynamic Tests of a Full ScaleCFT/BRB Composite Frame: Displacement Based Seismic Design and Response Evaluation.

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Center for Research on Earthquake Engineering, Taiwan, 2003; 165-176.

2. Leelataviwat S, Goel SC, Stojadinovic B. Drift and yield mechanism based seismic design andupgrading of steel moment frames. Research Report No. UMCEE 98-29. Department of Civil and

Environmental Engineering, University of Michigan, Ann Arbor, MI, 1998.

3. Lee SS, Goel SC. Performance-based design of steel moment frames using target drift and yield

mechanism. Research Report No. UMCEE 01-17. Department of Civil and Environmental Engineering,

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4. Housner GW. Limit design of structures to resists earthquakes. Proceedings of the World

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5. IBC. International Building Code, International Conference of Building Officials, Whittier,

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dynamic nonlinear analysis of two dimensional structures. Research Report No. UMCEE 96-21.Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI, 1996.

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